At what resistance does current cease to flow

[Elquery]

Howdy,

Pretty elementary question, I think. Looking at Ohm's law, current is I=V/R
For a given voltage (let's use 120 for typical U.S.A household) at what resistance will current actually cease to flow (equal zero)?

To clarify and expand on that: I am confused about whether a system with an open circuit (incomplete in regard to intentional conductors that is) will still find paths to slowly bleed current through, even though those paths are extremely high resistance. According to the equation, as resistance gets higher, current gets closer to zero, but never to zero. It would seem resistance would have to infinite for current to reach zero.

Are some things practically of such great resistance to act as though they're infinite? I am thinking along the lines of building materials like plastic conduit, drywall, insulation, etc)

 

[CWatters]

Your understanding is basically correct. There will be current flow unless the resistance is infinite, however the resistance of materials such as drywall is very high, and for most practical purposes it can be considered infinite. That doesn't necessarily mean any particular arrangement is "safe".

You can also get non linear effects where ohms law breaks down. For example air has a very high resistance but during a lightning strike very high currents can flow. The voltage can get so high that electrons are stripped from atoms and become available to conduct electricity.

 

[berkeman]

let's use 120 for typical U.S.A household

And since you seem to be asking about AC (like 60Hz AC), there will be a small AC leakage current that flows into the parasitic capacitance of the wiring. The longer the wires, and the closer they are spaced together and located close to metal objects, the larger the leakage current will be.

 

[jim hardy]

For a given voltage (let's use 120 for typical U.S.A household) at what resistance will current actually cease to flow (equal zero)?

Some of that is subjective ie "in the eye pf the beholder" .

You won't feel a few microamps so you will think current is zero,

Find a multimeter and set it for highest ohm scale.
Grab one lead with left hand, other with right hand. You'll probably read a few hundreds of thousands of ohms.
Then wet your fingers and repeat. The reading should drop tenfold, maybe more, depending on how calloused are your fingers.
But you won't feel any tingling because the current is so miniscule.

It would seem resistance would have to infinite for current to reach zero.

Mathematically that's quite so. Math is quite precise.
Real word measurements are always approximate - in house wiring a microamp might as well be zero..

 

[sophiecentaur]

Pretty elementary question, I think. Looking at Ohm's law, current is I=V/R

This, for me, is always problematical. Ohm's Law only applies to Linear Conductors. Although you can always find the ratio of V:I for any component, you may find the result can vary by a lot (just think of a tungsten filament light bulb). You can never assume that any real circuit is linear, right down to very low values of current (or up to very high values).
The great thing about EE is that most of the components we use (except the explicitly non-linear ones) will follow Ohm's Law over the normal range of conditions. Stray outside these conditions and you will find that an Open Circuit '∞Ω' can be more like a few thousand MΩ. Charge up a Van der Graaff generator on a damp day and it will only hold its charge for a few minutes. OTOH, some high voltage Capacitors are so 'good' that people tend to keep the terminals wired together to avoid lethal static voltages building up on them. (Also old CRT TV tubes.)

 

[Rive]

For a given voltage (let's use 120 for typical U.S.A household) at what resistance will current actually cease to flow (equal zero)?

A quite tricky question. In general, it will be zero only if there is no longer any relevant effect (you have to define what's relevant, and it has to be compliant with the safety rules). This can actually mean many things, and the limit will depend on the circumstances.

An interesting extension to this that sometimes when you have equipment sensitive enough you get effect even when there is no (intended) voltage (=> noise).

 

[Elquery]

great stuff to think about.

I'm not an electrical engineer nor electrician so a lot of this is virgin territory to me (such as non-linear effects).

While I wasn't initially asking for this reason, I am now curious about human bodies being added to a circuit as a parallel resistor. If current is flowing on, say, a 10 awg wire and I add a resistor in parallel, yet that resistor is 5,000 ohms (a theoretical resistance of human body under certain conditions) will some current flow through that resistor (body)? I am assuming the answer is; yes but not a lot...

I ask in part because people make the claim that if someone where to grab a 'hot' load wire (with current) with both hands, they would not feel a shock. Is the case simply that they are indeed 'seeing' current, but that the extremely low (comparative) resistance of the wire means only a very tiny amount of current is traveling through the body? Obviously this would not be safe since its possible the person could have lowered resistance for some reason or a wire connection could come loose or something etc.

 

[anorlunda]

Electric shock hazard is a complicated problem. But in general, yes it depends on the path through your body. The worst case might be if current enters in your hand, and exits from a bare foot on wet ground. But if the current has no place to go, no current flows in the body.

You may have seen images like this of linemen maintaining high voltage lines.

 

[berkeman]

While I wasn't initially asking for this reason, I am now curious about human bodies being added to a circuit as a parallel resistor. If current is flowing on, say, a 10 awg wire and I add a resistor in parallel, yet that resistor is 5,000 ohms (a theoretical resistance of human body under certain conditions) will some current flow through that resistor (body)? I am assuming the answer is; yes but not a lot...

The concept is called a "current divider". The current through each parallel resistor is inversely proportional to the resistance compared to the other parallel resistor(s). The 5000 Ohm resistance will have a very small current flowing through it compared to the parallel 0.001 Ohm wire resistance, but there will indeed be a non-zero current flowing through it. Hope that helps.

https://en.wikipedia.org/wiki/Current_divider

 

[Elquery]

The worst case might be if current enters in your hand, and exits from a bare foot on wet ground. But if the current has no place to go, no current flows in the body.

Thanks for the response.

In the example I am curious about, it is not a question of the current having a place to go, since I am proposing a situation where someone grabs onto a current carrying conductor with both hands (meaning there is undoubtedly a path from hand, through body, out hand. Essentially a parallel resistor. So the question becomes, is the current through that resistor (body) minuscule since the wire has WAY less resistance (and so it terms of voltage presents close to zero voltage potential between the two points on the conductor being grabbed onto).

 

[CWatters]

If we ignore his feet what matters is the voltage difference between one hand and the other. If his hands are close together on the same thick wire there won't be much voltage difference between them so little current will flow from one hand to the other.

However in most/many cases you wouldn't be able to ignore what his feet are connected to. I have had a pretty painful shock by touching 240VAC while wearing shoes.

 

[Rive]

The loads connected to line voltage are not expected to have impact on the line voltage itself (higher loads are expected to blow the fuse somewhere). So whatever wire it is, if it is the line voltage then usually you will have line voltage regardless the current. The 5kOhm in your example will meet the 120V, producing ~ 24mA current: and while that is not always deadly in short term, it is already in the range where you are not necessarily able to get yourself free.

 

[Elquery]

The current through each parallel resistor is inversely proportional to the resistance compared to the other parallel resistor(s).

Yes that clears it up, thank you! This is what I was assuming to be the case, but wanted some confirmation.

If his hands are close together on the same thick wire there won't be much voltage difference between them so little current will flow from one hand to the other.

Yes in terms of voltage this makes sense now.

 

[Elquery]

So whatever wire it is, if it is the line voltage then usually you will have line voltage regardless the current. The 5kOhm in your example will meet the 120V, producing ~ 24mA current

Now I'm a wee bit confused. Do you mean that you will meet the 120V with potential to ground (i.e. what CWatters is getting at in that you 'can't ignore what your feet are doing'). But from hand to hand the voltage potential would be near zero, correct?

However in most/many cases you wouldn't be able to ignore what his feet are connected to.

This unveils another lack of understanding on my part. I'm getting that the current flowing between hands would be tiny; whether we think of that as due to low voltage potential between points of the wire where the hands touch, or the low resistance of the wire compared to the human. But now I am wondering why/how current would have a viable path through the body into the ground ASSUMING that the wire we are touching is completing its circuit back at source. Wouldn't this be a similar situation as the hands on the wire, where the path through the body and through the actual ground would have so much resistance compared to the wire as to draw only minuscule currents (theory).

 

[Elquery]

It does get me wondering too now about why current from transmission lines would travel through someone to ground. Given my perhaps flawed (or at least incomplete) understanding that current wants to get back to source, how does a path into the ground (be it through a human or whatnot) provide a viable path back to the transformer/power-station (in comparison with the transmission line itself). I have a feeling that question gets quite a bit more complicated. We don't need to diverge too much if that's the case. Not trying to go down the rabbit hole and ask a million questions; just thinking out loud. Thanks for the thoughts

 

[Rive]

Do you mean that you will meet the 120V with potential to ground (i.e. what CWatters is getting at in that you 'can't ignore what your feet are doing'). But from hand to hand the voltage potential would be near zero, correct?

With both hands on the same wire, yes and yes. And it is really about what your feet are doing. And due safety reasons you should always assume that you are standing on the ground (or touching it somewhere).

This whole

...people make the claim that if someone where to grab a 'hot' load wire (with current) with both hands, they would not feel a shock...

business makes my hair stand on end.

 

[jim hardy]

However in most/many cases you wouldn't be able to ignore what his feet are connected to.

THAT is the catch-22 to his friend's argument. It's not whether he uses one or both hands, it's where are his feet ?

Age old question - How can a bird sit on a power line ?
Does it matter if Mr Bird uses one foot or two?

Old timer electricians tell beginners "Wear thick soled shoes and keep one hand in your pocket".

there are several old threads on house wiring...
https://www.physicsforums.com/threads/grounding-in-electrical-circuits.526008/#post-3480346
i tried to paint a word picture in post 15 there.

some more recent ones have images to help, many from @dlgoff

 

[jim hardy]

Given my perhaps flawed (or at least incomplete) understanding that current wants to get back to source, how does a path into the ground (be it through a human or whatnot) provide a viable path back to the transformer/power-station

easy - the transformer is tied to earth.
That's so the low side of your house wiring will be at about the same potential as the ground you're standing on.

And your concept, 'current (more correctly CHARGE) wants to get back to source' is right on. Bravo !

 

[anorlunda]

I think we've given good answers to the OP's question.

I get very nervous about public discussion of touching live wires on PF. For each correct way to do that that does not give a dangerous shock, there are a hundred ways for it to go wrong. Theoretical discussions, can lead to experimentation by young people who might read this thread.

Thread closed.